May Colloquium

In this paper, I will present a portrait of Frege as centrally concerned to make precise how scientific knowledge can be derived and expressed. At the core of this enterprise are Frege’s central linguistic innovations as these are embedded in the Begriffschrift, his conceptual notion. In this context, an issue appears to emerge when Frege applies logic to scientific subject-matter, starting with arithmetic: how is language representationally connected to content qua subject-matter? This problem is Leibniz’s Problem: it manifests itself as a problem about identity: Why doesn’t ‘2+3 = 5’ reduce to ‘5 = 5’ and thus express no mathematical content above and beyond the trivial? Frege rejects this as an error, but admits of a different puzzle, Frege’s Puzzle. This makes out the problem of identity as not about propositional content but about our cognitive relation to it, and how this gives rise to scientific knowledge. In Frege’s mature conceptual framework, the lesson of the puzzle of identity is that scientific inquiry is sensitive to the cognitive value of propositions (thoughts), where this notion is an aspect of Frege’s conception of judgement and the role of the recognition of truth in making judgements.